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Yup, this is my mental model too. Robots producing tons of stuff can never impoverish anybody. (This *ought* to be totally obvious). It's the monopolization of finite resources that is the killer. As usual, I'll refer whoever cares to Progress and Poverty. Henry George had this, and the solution, worked out over a hundred years ago.

The problem with standard neoclassical analysis is that it literally *defines* the long run to be the state in which all inputs are variable. Right off the bat, it precludes the student from thinking about natural resources. I don't know if this was a deliberate conspiracy perpetrated by the early neoclassicals on behalf of rentier interests. Georgists seem to think so. Somehow, for whatever reason, they managed to expunge land and with it the concept of rents (unearned income) from economics and the long run definition seems to be at the core of it.


"Robots producing tons of stuff can never impoverish anybody"

Not even in a model with heterogenous agents, with differential ownership of robots?

Haven't been able to spend etime on Nick's model, but think something's funny going on. Don't see how/why the total productivity of robots stays the same as the total productivity of labour across time. W isn't the issue. W*L is. But will hold back

K: the individual firm can vary all inputs, including land. But yes, the economy as a whole can't vary land. (So Long Run MC curves at the aggregate level will be much less elastic than at the individual firm level.)

But the lefty Sraffian model has only labour and time as inputs. If it was a conspiracy, it was a very big conspiracy. Nah, it's just townie kids, who think food comes from the supermarket, and think that rural idiocy is just a disappearing remnant of the past! Or maybe it's hard to separate out land and capital returns in National Income accounting, so Solow had to ignore land to do Solow Growth Accounting and build the Solow Growth model.


Change the production function to C + I = L + aK

We get Wh = 1 for human wages, Wr = a for robot wages, Price of one robot = 1, and Rc = a - g as before.

Im not sure what you are asking

If “a” stayed constant, you would want to expand them in a way that kept:

Pk*K/(1-b) = Pr*(R+L)/b

The percentage increase in R would be bigger than that of K (but the percentage increase of R+L would be the same).

If Pr decreased over time with g, I guess that you would want:


which imply:

Pk*K/(1-b)= (1+g/r)^-1*(L+R)/b

i.e. the ratio of K to L should increase by 1+g/r so if I haven’t done anything wrong (which I probably have), a high enough g/r ratio could keep wages up after all.

Ok – so if I´m correct in the reasoning above, I do see what you were after.

sloppy again.

It should read:

which was what I did in the calculations.

K: "Yup, this is my mental model too. Robots producing tons of stuff can never impoverish anybody. (This *ought* to be totally obvious). It's the monopolization of finite resources that is the killer."

This is like saying that "obviously" no one can be hurt by free trade - which "obviously" is wrong.

Assume a working market. Assume an additional supply of one billion uneducated workers. Assume that you are an uneducated worker -> not equal to profit. (or assume a supply of educated and uneducated workers without their own capital base, and non capital owners will be hurt).

Given market imperfection (such as unemployment benefits and sticky wages) it does not even have to create a Kaldor Hicks improvement. In the case with the linear production function, it would only create redistribution towards the rich and the really poor (that previously was withouta capital base).

That aside, the (given technology) finite recourse base is probably the bigger obstacle in the long run.

Not my day today. With the linear production function the additional supply obviosly dont have an effect on the wage. After today - I will start to think before I write.

With a leontief, the short run effect is simply redistribution.

nemi: you are doing fine. And making good progress. You are just thinking out loud.

Nick: Thanks

NR: "Do you eat 100 times as much rice as someone who lives on $1 per day?" No, I don't, of course. I thought that was the point I was trying to make. In fact, if part, or all of my income were redistributed downward, I would expect total demand for consumption goods to increase a bit. As income increases, consumption increases less rapidly, preference for investments moreso. I thought that this much was not controversial, so I didn't cite empirical evidence.

Could extremes of inequality hinder growth? Here's one reference: http://www.imf.org/external/pubs/ft/fandd/2011/09/Berg.htm

NR: "Until 2008, the last problem with the US was underconsumption! Overconsumption maybe."
I thought we put too much money into dot-coms and McMansions. At the time we thought they were investments, not consumption.

Ken: so what are people doing with the income? Holding cash? Is the income-elasticity of the demand for money much greater than one? If so, just print more money.

In other words, Krugman should have written the introduction to Asimov's The Naked Sun rather than The Foundation, in which the main character travels to a planet of 10,000 people living on giant robot-serviced latifundia.

Henry George came up with a model like yours in Progress and Poverty and comes to the conclusion that the trespassing class could only survive at the landlords' whims. Of course, once you concentrate land ownership, whether the workers are robots or low-paid humans is moot. I write more about it in my sig, but this is the gist of it.

LSTB: Interesting. I just read the bit you quoted from Henry George.

One *maybe* small criticism of Henry George: he *seems* (I may be wrong) to just *assume* (implicitly) that all new technology will be (what he calls) "labour saving". It isn't, and doesn't have to be. Some new technology is "land saving" (or "capital saving").

In my models, by supposing straight out that robots are identical to human workers, and that the only technological advance is in making robots cheaper to produce, I am making the same assumption. But I am fully aware that this is a very special assumption. If I stuck my parameter "a" in front of "N" (natural resources) in my model, instead of where I did stick it, I would get very different results. I was deliberately assuming (or trying to find) a nightmare scenario for labour.

Nick, you're right: George is missing land-saving capital, which is a point Mason Gaffney makes in his study guide. But George is also trying to find the nightmare scenario for labor, and it's fun to see him try before anyone had thought of robots. I'm not sure land-saving capital is relevant if you're positing that robots require the same sustenance as equivalent human workers.

The real-life fear with robots isn't that they're legitimized slavery but that they are cheaper and better than human workers, which creates a situation I can't imagine not benefiting land owners over non-land owners.


Yup. Right after hit submit I realized should have said "the representative worker" rather than "anyone."


"One *maybe* small criticism of Henry George: he *seems* (I may be wrong) to just *assume* (implicitly) that all new technology will be (what he calls) "labour saving""

The way I read George, he was talking about the asymptotic state of affairs. In the limit we can foresee robots dominating labour in all production, ie using less energy than humans to transform the same inputs (land) into products. But we cannot foresee them functioning without land or energy. In that limit the workers will earn nothing. Why would land owners waste any land/energy on workers, except as he points out, for charity.

In the end land can produce without workers. Workers can't produce without land.


Starting with robots, labor, and consumer goods

dR/dt = L * %L + R * %R
dC/dt = L * ( 1 - %L ) + R * ( 1 - %R ) = k * dL/dt

R = Robots
C = Consumer Goods
Y = Total Goods
L = Labor
k = Constant multiple of labor force equating growth in labor force to growth in consumer goods
%L = Percent of labor force tasked to building robots
%R = Percent of robot force tasked to building robots

dR/dt + dC/dt = L + R

R = a * exp ( b * t )
C = ( 1 - a ) * exp ( b * t )

Y = R + C = exp ( b * t )

dR/dt = ab * exp ( b * t )
dC/dt = ( b - ba ) * exp ( b * t )

dL/dt = ( b - ba ) * exp ( b * t ) / k
L = ( 1 - a ) * exp ( b * t ) / k

dR/dt = L * %L + R * %R
ab = ( 1 - a ) * %L / k + a * %R

k * dL/dt = L * ( 1 - %L ) + R * ( 1- %R )
b - ab = ( 1 - a ) * ( 1 - %L ) / k + a * ( 1- %R )

b = ( 1 - a ) / k + a = a * ( k - 1 ) / k + 1 / k

a * [ ( 1 - a ) / k + a = ( ak - a + 1 ) / k ] = ( 1 - a ) * %L / k + a * %R

Rearranging terms and solving for a:

a = [ k * %R - %L - 1 + sqrt ( ( k * %R - %L - 1 )^2 - 4 * %L * ( k - 1 ) ) ] / [ 2 * ( k - 1 ) ]

b = [ k * %R - %L + 1 + sqrt ( ( k * %R - %L - 1 )^2 - 4 * %L * ( k - 1 ) ) ] / [ 2 * k ]

"That sounds nightmarish, right? Because robots will get cheaper and cheaper, and drive down human wages?"

Only if you are trying to maximize robot production ( R ) will robots drive down human wages. If instead you are trying to maximize Y = R + C, then what %L and %R should you use ( hint maximize b )?

What you should find is that the percentage of labor dedicated to building robots ( %L ) should be 0% to maximize Y. The percentage of robots dedicated to building robots ( %R ) should be 100% to maximize Y. Even if robots can build consumer goods faster than the labor force, tasking robots to consumer goods will lead to a lower Y.

The obvious question is - What value does a robot that only builds other robots have?
And the answer is - Ask a robot.

Just I tiny little question regarding the Land and Robots model (I skipped the second one):

So, if one assumes that robots are perfect substitutes for workers and they earn the same wages (!!!!!)... what is it that makes robots, well, different from humans? I mean, other than Prof. Rowe's word.

Just sayin'!

Howdy! Do you happen to have any blogging education or it is a completely natural talent of yours? Thanks a bunch in advance for your answer.

This discussion has gotten me thinking about the political dimensions of robots. Here's my stab at a model.

Suppose we have two types of people, owners and workers.

The overall production function might look like this:

C + T + (P + D)/a + R + S = K + L

C is owners' share of consumption goods.
T is consumption goods transferred to the workers by the owners.
P is the production of new robots used to make consumer goods.
D is the production of new robots (drones) used for counter-insurgency.
R is the workers' level of insurgency.
S is the workers' leisure.
K is production robots.
L is labor.

Owners choose T, P, and D to maximize C while minimizing R, subject to constraints on K + L.
Workers choose R, S, and L to maximize T and S while minimizing D, subject to constraints on R + S + L.

I have no clue what the equilibrium looks like. The important thing to note is that the utility of each type depends on decisions made by the other type.

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